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A120568 Triangle, read by rows, where the k-th column equals the k-th self-composition of column 1 (A120567) for k>=0, such that row sums equal column 1. 2
1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 5, 6, 3, 1, 0, 15, 21, 12, 4, 1, 0, 53, 82, 54, 20, 5, 1, 0, 215, 351, 263, 110, 30, 6, 1, 0, 976, 1630, 1364, 644, 195, 42, 7, 1, 0, 4859, 8151, 7469, 3956, 1335, 315, 56, 8, 1, 0, 26150, 43627, 42971, 25304, 9505, 2470, 476, 72, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Paul D. Hanna, Rows n = 1..45, flattened.

EXAMPLE

The successive iterations of the g.f. of column 1 begin:

F(x) = x + x^2 + 2*x^3 + 5*x^4 + 15*x^5 + 53*x^6 + 215*x^7 + 976*x^8+...

F(F(x)) = x + 2*x^2 + 6*x^3 + 21*x^4 + 82*x^5 + 351*x^6 + 1630*x^7 +...

F(F(F(x))) = x + 3*x^2 + 12*x^3 + 54*x^4 + 263*x^5 + 1364*x^6 +...

F(F(F(F(x)))) = x + 4*x^2 + 20*x^3 + 110*x^4 + 644*x^5 + 3956*x^6 +...

F(F(F(F(F(x))))) = x + 5*x^2 + 30*x^3 + 195*x^4 + 1335*x^5 +9505*x^6+...

Triangle begins:

1;

0, 1;

0, 1, 1;

0, 2, 2, 1;

0, 5, 6, 3, 1;

0, 15, 21, 12, 4, 1;

0, 53, 82, 54, 20, 5, 1;

0, 215, 351, 263, 110, 30, 6, 1;

0, 976, 1630, 1364, 644, 195, 42, 7, 1;

0, 4859, 8151, 7469, 3956, 1335, 315, 56, 8, 1;

0, 26150, 43627, 42971, 25304, 9505, 2470, 476, 72, 9, 1;

0, 150585, 248631, 258976, 167804, 69899, 20023, 4207, 684, 90, 10, 1;

where column k equals the k-th self-composition of column 1.

PROG

(PARI) {ITERATE(n, F, p=#F)=local(G=x); for(i=1, n, G=subst(F, x, G+x*O(x^p))); G}

{T(n, k)=local(F=x+x*O(x^n), G=F, H=x); for(i=1, n, for(j=1, n, G=subst(F, x, G); H=H+x^j*G); F=H; G=x+x*O(x^n); H=G); polcoeff(ITERATE(k, F), n-k)}

for(n=1, 15, for(k=0, n-1, print1(T(n, k), ", ")); print(""))

CROSSREFS

Cf. A120567 (column 1).

Sequence in context: A110281 A120059 A067347 * A321960 A189233 A242153

Adjacent sequences: A120565 A120566 A120567 * A120569 A120570 A120571

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jun 14 2006

STATUS

approved

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Last modified November 27 12:40 EST 2022. Contains 358405 sequences. (Running on oeis4.)